If KL = 8x, LM = 14x - 6, and KM = 16, what is KL?

We are given that:

- \( KL = 8x \)
- \( LM = 14x - 6 \)
- \( KM = 16 \)

Since \( K, L, M \) lie on a straight line, the sum of \( KL \) and \( LM \) must equal \( KM \):

\[
KL + LM = KM
\]

Substitute the given expressions for \( KL \), \( LM \), and \( KM \):

\[
8x + (14x - 6) = 16
\]

Simplify the left-hand side:

\[
8x + 14x - 6 = 16
\]

\[
22x - 6 = 16
\]

Now, solve for \( x \):

\[
22x = 16 + 6
\]

\[
22x = 22
\]

\[
x = 1
\]

Now that we have \( x = 1 \), we can find \( KL \):

\[
KL = 8x = 8(1) = 8
\]

Thus, \( KL = 8 \).

Would you like further details on this solution? 

Here are some related questions for you to explore:
1. What is the value of \( LM \) when \( x = 1 \)?
2. What is the total length of \( KL + LM \)?
3. How would the result change if \( KM = 20 \) instead of 16?
4. Can you represent this problem geometrically on a number line?
5. What would happen if \( LM = 10x + 2 \) instead?

**Tip:** When dealing with line segments, always remember that the sum of smaller segments must equal the total length of the larger segment.

Learn how to solve for KL in the equation KL = 8x, LM = 14x - 6, and KM = 16. This algebra problem involves solving for x in a linear equation and understanding the segment addition postulate. Suitable for students in Grades 6-8.

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